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Understanding jump discontinuity in disordered system.

Anjan Daimari1, Diana Thongjaomayum1

  • 1Tezpur University, Department of Physics, Assam 784028, India.

Physical Review. E
|May 16, 2026
PubMed
Summary

Understanding critical points in complex systems is challenging due to broken jumps in order parameters. This study analyzes hysteretic responses in dilute Ising spin systems, revealing how varying coordination numbers influence magnetization jumps near critical fields.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Complex systems exhibit jump discontinuities in order parameters near critical points when subjected to external forces.
  • These discontinuities often break into smaller jumps, complicating the precise identification of critical points through simulations alone.

Purpose of the Study:

  • To investigate the phenomenon of broken jumps in the hysteretic response of a classical Ising spin system.
  • To understand the influence of dilution and varying coordination numbers on the magnetization curve in a nonequilibrium random field Ising model.

Main Methods:

  • Exact solution of the magnetization curve (m(h) vs h) for a dilute Bethe lattice with coordination number z=4.
  • Analysis of magnetization for sublattices with varying coordination numbers (z=4, 3, 2, 1, 0).
  • Testing the model on cubic lattices where exact results are unavailable.

Main Results:

  • The total magnetization discontinuity arises from the superposition of jumps from sites with different coordination numbers (z).
  • These superimposed jumps occur at the same critical external field (h_crit).
  • Sites with higher concentration and larger z contribute dominantly to the jump, with z≥3 sites being crucial for large jumps.

Conclusions:

  • The study provides an exact solution for the hysteretic response in dilute Ising spin systems, explaining broken jumps.
  • The findings elucidate the role of varying coordination numbers and site dilution in magnetization behavior.
  • This analysis aids in interpreting fluctuations around critical jumps in numerical simulations and experimental studies.